scientific article; zbMATH DE number 3065066

Publication date: 1951

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

prime number theorem Diophantine equations elementary number theory table of first 150 primes table of fundamental solutions for Pell equation table of primitive roots

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Cubic and quartic Diophantine equations (11D25) Higher degree equations; Fermat's equation (11D41) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01) Elementary number theory (11Axx)

Related Items

The second largest prime divisor of an odd perfect number exceeds ten thousand, The problem of the extension of D(4)-triple {1, b, c}, The number of irregular Diophantine quadruples for a fixed Diophantine pair or triple, Odd perfect numbers are greater than $10^{1500}$, Unnamed Item, Large 2-transitive arcs, Semisymmetric elementary Abelian covers of the Möbius-Kantor graph, On the number of prime factors of an odd perfect number, Outline of a Proof that Every Odd Perfect Number has at Least Eight Prime Factors, On the solvability of the Diophantine equation ${ax^2+by^2+cz^2=0 }$ in imaginary Euclidean quadratic fields, On a Number-Theoretic Result of Sylvester-Kronecker-Zsigmondy, Unnamed Item, Sommes courtes de certaines fonctions multiplicatives, A new variant of the Hilbert-Waring problem, Comparing multiplicative orders mod $p$, as $p$ varies, On polynomial solutions of Pell's equation, On circulant nut graphs, Unnamed Item, A survey on coefficients of cyclotomic polynomials, An Arithmetic Proof of a Theorem of Chan, Long, and Yang, A triangle-free, 4-chromatic $\mathbb{Q}^3$ Euclidean distance graph Scavenger hunt!, Triangular Diophantine tuples from {1, 2}, On $D(-1)$-triples $\{1,4p^2+1,1-p\}$ in the ring $\mathbb{Z}[\sqrt{-p}$ with a prime $p$], A New Look at an Old Equation, AN AMAZING IDENTITY OF GAUSS AND JENKINS’ LEMMA, A note on cubic residues modulo $n$, Ambiguous solutions of a Pell equation, Minimal degree of an element of a number field with respect to its quadratic extension, Squares in recurrences using elliptic curves, Computing Elliptic Curves over $$\mathbb{Q}$$ : Bad Reduction at One Prime, Simultaneous Pellian equations, Proof of the conjecture of Keskin, Siar and Karaatli, Bounds for Integral Solutions of Diagonal Cubic Equations, Metrical Theorems on Fractional Parts of Sequences, Unnamed Item, Computing elliptic curves over $\mathbb {Q}$, Unnamed Item, Rings of Integer-Valued Continuous Functions, Diophantine quadruples and near-Diophantine quintuples from P3,K sequences, On the Divisibility of an Odd Perfect Number by the Sixth Power of a Prime, Genus character L‐functions of quadratic orders and class numbers, There is no Diophantine quintuple, Infinitesimal and global rigidity and inflexibility of surfaces of revolution with flattening at the poles, Unnamed Item, Hopf algebras and congruence subgroups, On the solvability of the simultaneous Pell equations x2 − ay2 = 1 and y2 − bz2 = v12, On the Diophantine equation x 2 − kxy + y 2 − 2 n = 0, Hill and toda curves, Odd perfect numbers have at least nine distinct prime factors, Unnamed Item, On totally reducible binary forms. I, Spin models constructed from Hadamard matrices, ON VANISHING CRITERIA THAT CONTROL FINITE GROUP STRUCTURE II, On Multiple Prime Divisors of Cyclotomic Polynomials, Twist‐minimal trace formulas and the Selberg eigenvalue conjecture, Unnamed Item, On the simultaneous Pell equationsx²− (4m²− 1)y²=y²−pz²= 1, Uniform Distribution of Sequences of Integers, Elementary methods in the study of the distribution of prime numbers, A Lower Bound for the Set of Odd Perfect Numbers, On the Largest Prime Divisor of an Odd Perfect Number, The Smallest Nontrivial Solution to xk≡1 (modn) and Related Sequences, A Search Procedure and Lower Bound for Odd Perfect Numbers, Le problème de Tchébychev pour le douzième polynôme cyclotomique, Exponential sums with reducible polynomials, Parameter Determination for Complex Number-Theoretic Transforms Using Cyclotomic Polynomials, On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoids, The extensibility of the $D(\pm k)$-triple $\{k\mp 1,k, 4k\mp 1\}$, Spin models on finite cyclic groups, On the generalized Ramanujan-Nagell equation $x^2+(3m^2+1)=(4m^2+1)^n$, Statistical properties of half-$\ell$-sequences, Zeros of Racah coefficients and the Pell equation, Random numerical semigroups and a simplicial complex of irreducible semigroups, Prime factorization for values of cyclotomic polynomials in ${\mathbb Z}[i$], Averages of completely even arithmetical functions (over certain types of plane regions), Contributions à la théorie des corps et des polynômes cyclotomiques, On birational transformations of Hilbert schemes of points on $K3$ surfaces, Arithmetically independent integers and values of rational functions, A property of primitive prime divisors of $\Phi_ d (a)$, On the near prime-order MNT curves, $D(-1)$-triples of the form $\{1,b,c\}$ in the ring $\mathbb Z[\sqrt{-t}$, $t>0$], A $q$-analogue of the (J.2) supercongruence of van Hamme, On the exponential Diophantine equation $(a^n-2)(b^n-2)=x^2$, Classification of regular embeddings of hypercubes of odd dimension, Arithmetische Eigenschaften von Galois-Räumen. I, Infinite products involving Dirichlet characters and cyclotomic polynomials, Embedding Euclidean distance graphs in $\mathbb{R}^n$ and $\mathbb{Q}^n$, 2-adic cofiltration of $\mathrm{SO}_3(\mathbb{Q})$, On the Diophantine equation $x^2-kxy+ky^2+ly=0$, $l\in\{1,2,4,8\}$, Quadratic forms and elliptic curves. IV, Integral points on a certain family of elliptic curves, On groups generated by involutions of a semigroup., Compact representation of quadratic integers and integer points on some elliptic curves, On a class of quartic Thue equations with three parameters, On the value of Gaussian sums, Vandermonde matrices with nodes in the unit disk and the large sieve, On Huppert's conjecture for $G_2(q)$, $q\geq 7$., Maximal ranks and integer points on a family of elliptic curves. II., Quadratic cyclic sequences, Simultaneous concentrations of additive functions, Inhomogeneous quadratic congruences, $q$-analogs of some congruences involving Catalan numbers, On prime power order elements of general linear groups., Hidden symmetry and the number-theoretic structure of the energy levels of a perturbed harmonic oscillator, A unified quantum $SO(3)$ invariant for rational homology 3-spheres, A note on a recent paper of Iwasawa on the capitulation problem, The Hilbert function of curves on certain smooth quartic surfaces, Regular maps with nilpotent automorphism groups, Randomized function evaluation on a ring, Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras., Manin's conjecture for quartic del Pezzo surfaces with a conic fibration, On certain $D(9)$ and $D(64)$ Diophantine triples, Arithmetic progressions on Pell equations, A note on Pépin's counterexamples to the Hasse principle for curves of genus 1, On the Thue-Vinogradov lemma, Classes of gap balancing numbers, Generalized version of the characteristic number of two simultaneous Pell's equations, On quadratic solutions of $x^4+py^4=z^4$, On the eigenvalues of distance powers of circuits, Cryptanalysis of a quadratic knapsack cryptosystem, Multiply perfect numbers, Mersenne primes, and effective computability, On the Diophantine equation $\frac{x^3-1}{x-1}=\frac{y^n-1}{y-1}$, Factors of the Gaussian coefficients, Class number one criteria for real quadratic fields. II, On an assertion of Ramanujan concerning binary quadratic forms, Almost powers in short intervals, Integral points on the elliptic curve $E_{ pq }$: $y^2 = x^3 + ( pq - 12) x - 2( pq - 8)$, Diophantine triples with largest two elements in common, On the Diophantine pair $\{a,3a\}$, Monogenic cyclotomic compositions, Quelques résultats sur les diviseurs fixes de l'index des nombres entiers d'un corps algébrique, On $n$-dimensional Kloosterman sums, On simple generators of recursively enumerable languages, Punktfolgen auf Kurven und Flächen, Finite groups with Abelian Sylow 2-subgroups of order 8, Sur les discriminants des nombres algébriques, Remarques sur les formes à plusieurs variables décomposables en facteurs linéaires, The characterization of finite groups with dihedral Sylow 2-subgroups. I, II, The characterization of finite groups with dihedral Sylow 2-subgroups. III, Uniform distribution of polynomial-generated sequences in $GF[q,x$], On the number of roots of an integral polynomial modulo $q$, Pellian equations of special type, Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods, Remarques sur une catégorie d'équations diophantiennes à deux indéterminées, Quelques problèmes relatifs aux unités algébriques, Positive integer solutions of some Diophantine equations in terms of integer sequences, Diophantine $m$-tuples and elliptic curves, Odd, spoof perfect factorizations, Criteria for $n$-th power residues, Über die Summe $\sum_{n \leqq x}\varphi(f(n))$ und verwandte Probleme, Infinite families of reciprocal monogenic polynomials and their Galois groups, On Legendre's equation $ax^2+by^2+cz^2=0$, A system of Pellian equations and related two-parametric family of quartic Thue equations, On the Diophantine equation $ax^2+by^2=ck^n$, Establishing the minimal index in a parametric family of bicyclic biquadratic fields, The Hoggatt-Bergum conjecture on $D(-1)$-triples $\{F_{2k+1}$, $F_{2k+3}$, $F_{2k+5}\}$ and integer points on the attached elliptic curves, Ratio balancing numbers, The simultaneous diophantine equations $5Y^ 2-20=X^ 2$ and $2Y^ 2+1=Z^ 2$, Die Berechnung der dritten Einheitswurzeln in Restklassenkörpern, Pair correlation of values of rational functions (mod $p$), Further results on periods and period doubling for iterates of the trapezoid function, Goldbach problem in polynomial values, An absolute bound for the size of Diophantine $m$-tuples, Polynomials providing a residue class mapping for each natural module, Hyper-Kähler manifolds, General solutions of sums of consecutive cubed integers equal to squared integers, Sums of consecutive squares which result in a square